The present invention is related to an apparatus and a nondestructive method for determining the porosity of a layer or part of a layer formed on a substrate. The porosity and particularly the pore size distribution defines the mechanical, thermal and chemical properties of the porous materials. For example, by knowing the pore size distribution, one has a clear indication of the compatibility of this layer with the manufacturing process of integrated circuits or liquid crystal displays.
The ongoing miniaturization in integrated circuits with increased complexity and multilevel metal layers and the focus on increasing speed of these circuits has increased the demand for low permittivity materials, particularly for use as intermetal dielectric layers. Conventionally, metal interconnects, mostly aluminum layers, with silicon dioxide as intermetal dielectric are used, but this conventional solution will not be able to meet the stringent specifications resulting from the above mentioned trends. Therefore, to avoid that the larger portion of the total circuit delay is caused by the resistance and capacitance of the interconnect system, the permittivity of the dielectric used has to be reduced. This is stated in numerous publications, e.g. in Table 1 of R. K. Laxman, xe2x80x9cLow ∈ dielectric: CVD Fluorinated Silicon Dioxidesxe2x80x9d, Semiconductor International, May 1995, pp. 71-74. Therefore miniaturization has lead to an intensified search for new low K materials. A low c material, a low K material and a material with a low permittivity are all alternative expressions for a material with a low dielectric constant, at least for the purposes of this disclosure.
Part of the search for new low K materials has been directed to changing the properties of silicon dioxide as deposited. Besides the focus has been on changing the properties of silicon oxide, there is an ongoing search for new low K materials. Among these new materials are the organic spin-on materials, having a K value in the range from 2.5 to 3, and the inorganic low-K materials as e.g. xerogels having a K value typically lower than 1.5. An important characteristic of these new materials is their porosity, i.e. the volumes of the pores as well as the pore size distribution. The relative pore volume directly defines the permittivity value and can be estimated by measurement of the dielectric constant using spectroscopic ellipsometry and porosity/density simulation as e.g. in T.Ramos et al., xe2x80x9cLow-Dielectric Constant Materialsxe2x80x9d, Mater. Res. Soc. Proc. 443, Pittsburgh, Pa. 1997, p.91. However, it is much more difficult to measure the pore size distribution. The pore size distribution defines mechanical, thermal and chemical properties of the porous materials. Therefore, by knowing the pore size distribution, one has a clear indication of the compatibility of the material with the manufacturing process of integrated circuits. If the pores are open, information about the pore size distribution can be obtained by adsorption porometry.
Adsorption porometry is based on the well-known phenomenon of hysteresis loop that appears in the processes of capillary condensation and desorption of vapour out of porous adsorbents. The theory of capillary condensation, as in S. J. Gregg and S. W. Sing, xe2x80x9cAdsorption, Surface Area and Porosityxe2x80x9d, Acad. Pr., N.Y., 1982, explains the appearance of hysteresis by the change in the equilibrium vapour pressure above the concave meniscus of the liquid. Vapour can condense in the pores of a solid substrate even if its relative pressure is below unitary value, i.e. there is condensation even when the vapour pressure is less than the atmospheric pressure. Dependence of the relative pressure on the meniscus curvature is described by Kelvin equation:
In(P/P0)=xe2x88x922xcex3VL/rmRT,
where P/P0 is the relative pressure of the vapour in equilibrium with the liquid, the surface of the liquid being a meniscus with the curvature radius rm; xcex3and VL are the surface tension and molar volume of the liquid adsorbate, respectively. The curvature radius rm is close to the pore radius. Adsorption-desorption hysteresis appears if the radius of curvature of the meniscus of the condensing liquid is changed as a result of adsorption. Every P/P0 value corresponds to a definite rm. Only spheroidal menisci are formed during desorption, while adsorption results in either spheroidal or cylindrical menisci. Because of this, it is more convenient to use desorption isotherms to determine the effective size of pores equivalent to cylindrical ones.
A method of wide application is adsorption porometry with the use of liquid nitrogen as in S. J. Gregg et al., xe2x80x9cAdsorption, Surface Area and Porosityxe2x80x9d, Acad. Pr., N.Y., 1982. This state-of-the-art method is however only applicable when analyzing large samples because this method is based on direct weighing of the samples during the vapour adsorption and desorption. Therefore, this destructive method is inappropriate for analyzing thin films formed on a substrate. In some cases, in order to characterize the pore size distribution using this state-of-the-art method, it is necessary to damage the films of several tens of substrates. Moreover, the very low temperature which is required for nitrogen porometry also creates additional problems.
In an aspect of the invention a method is disclosed for determining the porosity of an element formed on a substrate, said substrate being positioned in a pressurized chamber, said chamber being at a predetermined pressure and at a predetermined temperature, said method comprising the steps of:
admitting a gaseous substance in said chamber; and
determining after a predetermined period of time the porosity of said element by means of at least on ellipsometric measurement.
For instance, the gaseous substance can be a vapour, or a gas or a mixture thereof. An appropriate gaseous substance is a substance which is at a predetermined temperature and a predetermined pressure (preferably at a pressure below the equilibrium vapour pressure of said gaseous substance) present both as a gaseous substance is well as condensed gaseous substance. The gaseous substance is preferably selected such that the interaction between the condensed gaseous substance and the thin film is as limited as possible. More preferably, said predetermined temperature is room temperature. An example of said element formed on said substrate is a thin film, particularly a thin film of an organic or inorganic material, preferably, with a low dielectric constant.
In an embodiment of the invention, said predetermined period of time is chosen such that in said chamber equilibrium is established between said gaseous substance and the condensed form of said gaseous substance.
In an embodiment of the invention a method is disclosed for determining the porosity of an element formed on a substrate comprising the steps of:
selecting a gaseous substance being admissible to an exposed surface of the element formed on the substrate, said substrate being positioned in a pressurized chamber at a predetermined constant temperature;
setting the pressure in the chamber to a first predetermined value;
admitting said gaseous substance in said chamber, the temperature of the gaseous substance being substantially identical to said predetermined constant temperature;
after a predetermined period of time measuring the value of the pressure in the chamber and performing an ellipsometric measurement to determine the optical characteristics of the element;
changing the pressure in the chamber in a stepwise manner, whereby after each step and after a predetermined period of time the optical characteristics are determined by means of an ellipsometric measurement, to thereby determine an adsorption-desorption isotherm; and
calculating the porosity using at least the measured optical characteristics and the adsorption-desorption isotherm.
In another aspect of the invention an apparatus is disclosed for determining the porosity of an element formed on a substrate, said apparatus comprising:
a pressurized chamber in which said substrate is positionable;
a temperature control element for fixing the temperature in said chamber at a predetermined value;
a pump for changing the pressure in said chamber;
a supply for admitting a gaseous substance;
an ellipsometer for determining the optical characteristics of said element;
at least a first controllable component and at least a second controllable component, said first component being positioned between said pump and said chamber and allowing a precise control of the pressure in the chamber, said second component being positioned between said supply and said chamber and allowing a precise control of the flow of said gaseous substance into said chamber; and wherein the porosity is calculated from said optical characteristics. Particularly the inner walls of said chamber are composed of a material with a porosity which is substantially lower than the porosity of the element to be analysed.
In another embodiment of the invention, the apparatus can further comprise a control element and a recording element. The control element controls the first and second component. The recording element allows to record the pressure in the chamber, the optical characteristics and the adsorption-desorption curve thereby enabling the calculation of the porosity of the element.
In another embodiment of the invention an apparatus is disclosed for determining the porosity of an element formed on a substrate wherein said second controllable component is a microvalve being composed of at least a first material and a second material, said first material being conductive, said second material being elastic and wherein said first material and said second material have a substantially different thermal expansion coefficient.